The following information (and advice) is contained in a post-em from Curt Hofemann, curt_hofemann@@yahoo.com:
Hie thee to Stewart Baldwin's "Henry Project" for scholarly research on this person (& much more):
http://sbaldw.home.mindspring.com/hproject/henry.htm
Baldwin III ruled briefly as joint count with his father Arnulf I, but died before his father. Count Baldwin's name appears in lists of abbots of St. Bertin [Monumenta Germaniae Historica, Scriptores series, 13, 391, 607], and he would appear to have held that office for a short period before his death. [Ref: Henry Project]
Possible illegitimate son (status uncertain):
Ascelin (Azelin) or Albert de Tronchiennes, bishop of Paris, 1016-1018.
The History of the Bishops of Cambrai states that Ascelin (or Albert, as he is called in some sources) was an illegitimate son of count Baldwin of Flanders. [Gesta Episcoporum Cameracensium, MGH SS 7, 448]. If this is accurate, Baldwin III would be the only count of Flanders named Baldwin who would make a chronologically feasible father for Ascelin. [LEon Vanderkindere, La Formation Territoriale des Principautes Belge au Moyen Age (2 vols., 2nd ed., Brussels, 1902, reprinted 1981) 1, 293], lists Ascelin as a son of Baldwin, without citing a source, but neither Erich Brandenburg, Die Nachkommen Karls des GroÆen (Frankfurt, 1964) norKarl Ferdinand Werner, 'Die Nachkommen Karls des GroÆen bis um das Jahr 1000 (1.-8. Generation)', Karl der GroÆe 4 (1967) mention him. His biography in Dictionnaire de Biographie FranAaise 3, 1238-40 states that he was very probably the son of Arnulf I, and then contradicts this statement by calling Arnulf II a brother of Ascelin. The DBF article makes Ascelin a provost of the monastery of Saint-Marie in Tronchiennes as early as 951, which, if true, would chronologically rule out Ascelin's affiliation as a son of Baldwin III. However, this date is suspicious, as it is 65 years before Ascelin became bishop, and the next event mentioned in the biography is in 995. [Ref: Henry Project]
Falsely attributed daughters:
Bertha (existence doubtful), m. Aymar, count of GenEve (existence doubtful). [P. Anselme, Histoire Genealogique et Chronologique de la Maison Royale de France, ... (1726), 2, 715. She has also been falsely attached to Baldwin's father Arnulf I.]
Jeanne, mother of Wolbodo, bishop of LiEge. [LEon Vanderkindere, La Formation Territoriale des Principautes Belge au Moyen Age (2 vols., 2nd ed., Brussels, 1902, reprinted 1981), 1, 293, citing Meyer, Rerum Flandr., 67, with a remark that the attribution is in error] [Ref: Henry Project]
Regards,
Curt